naginterfaces.library.machine.complex_​safe

naginterfaces.library.machine.complex_safe()

complex_safe returns the safe range of complex floating-point arithmetic.

For full information please refer to the NAG Library document for x02an

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/x02/x02anf.html

Returns

zrangefloat

The safe range of complex floating-point arithmetic.

Notes

complex_safe is defined to be the smallest positive model number $z$ such that for any $x$ in the range [$z,1/z$] the following can be computed without undue loss of accuracy, overflow, underflow or other error:

$-w$

$1/w$

$-1/w$

$\sqrt{w}$

$\log \left(w\right)$

$exp\left(\log \left(w\right)\right)$

$y^{\left(\log \left(w\right)/\log \left(y\right)\right)}$ for any $y$

$\left|w\right|$

where $w$ is any of $x$, $ix$, $x+ix$, $1/x$, $i/x$, $1/x+i/x$, and $i$ is the square root of $-1$.